Gertrude asks Lord Goring to accompany Mabel to the art exhibit, and then asks Mabel if she minds. When Mabel replies, you can see the reflection of Gertrude in the mirror behind Mabel. But you shouldn't be able to see Gertrude since she is seated during the entire scene.
Lord Goring's jacket is buttoned, then unbuttoned, then buttoned again as he explains Lady Chiltern's letter to Lord Chiltern, Mabel and Lady Chiltern herself near the end of the film.
The Speaker is shown calling MPs to speak by naming their constituency ("The Honourable Member for Witney" etc). British MPs do address each other in this way, but the Speaker calls MPs to speak by naming them personally.
Several MPs including Lord Caversham are shown wearing top hats in Parliament. MPs didn't (and still don't) wear hats during a session of the House, unless they are raising a Point of Order while a vote is in progress.
In the establishing shot for the scenes in the House of Commons, the Palace of Westminster is shown from Westminster bridge but the Ayrton light is not lit. Since 1885 when either house is sitting after nightfall a green light should be visible above the clock face.
Lord Goring is referred to at one point as "Lord Arthur Goring", not as "Arthur, Lord Goring", as would be correct, and when Mabel talks of getting married, he says "Who to?" - a Lord would surely be well-educated enough to know it should be "Whom to?" to be grammatically correct.
The closing scene of 'The Importance of Being Earnest' is shown as taking place in a garden. That is the setting for Act 2; the final Act 3 takes place in 'The Morning-Room of the Manor-House, Woolton'.
At the reception at the Chiltern's home, Sir Robert is requested to meet the Indian Ambassador. In 1895 India was a British possession and there could not be such an Ambassador who represents only independent states.
When Arthur's father arrives just as he is leaving for the art exhibition, the camera hits a large vase of orange flowers as it moves to the right, causing them to flutter and move.